Paper: arXiv 2602.00858

Authors: Tim Leung, Matthew Lorig

Abstract

We price European options in a class of models in which the volatility of the underlying risky asset depends on the short rate of interest. Our study results in an explicit pricing formula that depends on knowledge of a characteristic function. We provide examples of models in which the characteristic function can be computed analytically and, thus, the value of European options is explicit. Numerical implementation to produce the implied volatility is also presented.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 2.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical framework using Girsanov measure transforms and Fourier inversion to price options under short-rate-dependent volatility models. However, it lacks empirical validation, empirical data backtesting, or calibration to market data, relying strictly on analytical derivations and synthetic implied volatility plots.

Research Flowchart

  flowchart TD
    A[Goal: Price European Options with Short-Rate-Dependent Volatility] --> B[Model Formulation: Link Underlying Asset Volatility to Short Rate]
    B --> C[Derive Analytical Characteristic Function]
    C --> D[Apply Fourier Inversion for Option Pricing Formula]
    D --> E[Numerical Implementation & Calibration]
    E --> F[Outcomes: Explicit Option Prices & Implied Volatility Surfaces]

Cited References (17)

  1. Explicit formulas for L aplace transforms of stochastic integrals (2008)
  2. A Theory of the Term Structure of Interest Rates (1985) — link
  3. An interest rate model with upper and lower bounds (2002) — link
  4. Explicit Implied Volatilities for Multifactor Local-Stochastic Volatility Models (2017) — link
  5. A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options (1993) — link
  6. Option Valuation Using the Fast F ourier Transform (1999) — link
  7. Transform Analysis and Asset Pricing for Affine Jump-Diffusions (2000) — link
  8. Empirical Performance of Alternative Option Pricing Models (1997) — link
and 9 more
  1. PDE and Martingale Methods in Option Pricing (2011) — link
  2. On the H eston Model with Stochastic Interest Rates (2011) — link
  3. What Explains the Stock Market’s Reaction to F ederal R eserve Policy? (2005) — link
  4. Do Actions Speak Louder Than Words? T he Response of Asset Prices to Monetary Policy Actions and Statements (2005)
  5. Risk, Uncertainty and Monetary Policy (2013) — link
  6. The VIX , the Variance Premium and Stock Market Volatility (2014) — link
  7. The Effects of F ederal Funds Rate Surprises on S&P 500 Volatility and Volatility Risk Premium (2012) — link
  8. When No News Is Good News — T he Decrease in Investor Fear after the FOMC Announcement (2017) — link
  9. Market Volatility, Monetary Policy and the Term Premium (2017) — link

0 of 17 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.